Search results for "singular"
showing 10 items of 589 documents
Generic 3-parameter families of vector fields on the plane, unfolding a singularity with nilpotent linear part. The cusp case of codimension 3
1987
AbstractA cusp type germ of vector fields is a C∞ germ at 0∈ℝ2, whose 2-jet is C∞ conjugate toWe define a submanifold of codimension 5 in the space of germs consisting of germs of cusp type whose 4-jet is C0 equivalent toOur main result can be stated as follows: any local 3-parameter family in (0, 0) ∈ ℝ2 × ℝ3 cutting transversally in (0, 0) is fibre-C0 equivalent to
Orthogonality Catastrophe and Decoherence in a Trapped-Fermion Environment
2012
The Fermi edge singularity and the Anderson orthogonality catastrophe describe the universal physics which occurs when a Fermi sea is locally quenched by the sudden switching of a scattering potential, leading to a brutal disturbance of its ground state. We demonstrate that the effect can be seen in the controllable domain of ultracold trapped gases by providing an analytic description of the out-of-equilibrium response to an atomic impurity, both at zero and at finite temperature. Furthermore, we link the transient behavior of the gas to the decoherence of the impurity, and, in particular to the amount of non-markovianity of its dynamics.
Decadal time scale variability recorded in the Quelccaya summit ice core δ 18 O isotopic ratio series and its relation with the sea surface temperatu…
1998
The spectral characteristics of the delta /sup 18/O isotopic ratio time series of the Quelccaya ice cap summit core are investigated with the multi taper method (MTM), the singular spectrum analysis (SSA) and the wavelet transform (WT) techniques for the 500 y long 1485-1984 period. The most significant (at the 99.8% level) cycle according to the MTM F-test has a period centered at 14.4 y while the largest variance explaining oscillation according to the SSA technique has a period centered at 12.9 y. The stability over time of these periods is investigated by performing evolutive MTM and SSA on the 500 y long delta /sup 18/O series with a 100 y wide moving window. It is shown that the cycle…
Coherent quasiparticle approximation (cQPA) and nonlocal coherence
2010
We show that the dynamical Wigner functions for noninteracting fermions and bosons can have complex singularity structures with a number of new solutions accompanying the usual mass-shell dispersion relations. These new shell solutions are shown to encode the information of the quantum coherence between particles and antiparticles, left and right moving chiral states and/or between different flavour states. Analogously to the usual derivation of the Boltzmann equation, we impose this extended phase space structure on the full interacting theory. This extension of the quasiparticle approximation gives rise to a self-consistent equation of motion for a density matrix that combines the quantum…
Mössbauer gamma-ray diffraction from the molecular crystal KCN
1980
Abstract Mossbauer gamma-ray diffraction was applied to separate the elastic and inelastic scattering intensities from the (200), (400) and (600) Bragg reflections of KCN. The energy resolution of our experiment was 60 neV. The Debye-Waller factor extracted from the elastic data and the thermal diffuse inelastic data both increase towards phase transition, theoretically a logarithmic singularity was predicted.
Subwavelength beams with polarization singularities in plasmonic metamaterials
2014
We investigated the diffraction behavior of plasmonic Bessel beams propagating in metal-dielectric stratified materials and wire media. Our results reveal various regimes in which polarization singularities are selectively maintained. This polarization-pass effect can be controlled by appropriately setting the filling factor of the metallic inclusions and its internal periodic distribution. These results may have implications in the development of devices at the nanoscale level for manipulation of polarization and angular momentum of cylindrical vector beams. This research was funded by the Spanish Ministry of Economy and Competitiveness under the project TEC2011-29120-C05-01.
Non-Homogeneity of Lateral Resolution in Integral Imaging
2013
We evaluate the lateral resolution in reconstructed integral images. Our analysis takes into account both the diffraction effects in the image capture stage and the lack of homogeneity and isotropy in the reconstruction stage. We have used Monte Carlo simulation in order to assign a value for the resolution limit to any reconstruction plane. We have modelled the resolution behavior. Although in general the resolution limit increases proportionally to the distance to the lens array, there are some periodically distributed singularity planes. The phenomenon is supported by experiments.
Singular systems in dimension 3: Cuspidal case and tangent elliptic flat case
2007
We study two singular systems in R3. The first one is affine in control and we achieve weighted blowings-up to prove that singular trajectories exist and that they are not locally time optimal. The second one is linear in control. The characteristic vector field in sub-Riemannian geometry is generically singular at isolated points in dimension 3. We define a case with symmetries, which we call flat, and we parametrize the sub-Riemannian sphere. This sphere is subanalytic.
Positive solutions for singular (p, 2)-equations
2019
We consider a nonlinear nonparametric Dirichlet problem driven by the sum of a p-Laplacian and of a Laplacian (a (p, 2)-equation) and a reaction which involves a singular term and a $$(p-1)$$ -superlinear perturbation. Using variational tools and suitable truncation and comparison techniques, we show that the problem has two positive smooth solutions.
Positive solutions for parametric singular Dirichlet(p,q)-equations
2020
Abstract We consider a nonlinear elliptic Dirichlet problem driven by the ( p , q ) -Laplacian and a reaction consisting of a parametric singular term plus a Caratheodory perturbation f ( z , x ) which is ( p − 1 ) -linear as x → + ∞ . First we prove a bifurcation-type theorem describing in an exact way the changes in the set of positive solutions as the parameter λ > 0 moves. Subsequently, we focus on the solution multifunction and prove its continuity properties. Finally we prove the existence of a smallest (minimal) solution u λ ∗ and investigate the monotonicity and continuity properties of the map λ → u λ ∗ .